journal article·2015-06

Addressing Memory and Speed Problems in Nondestructive Defect Characterization: Element-by-Element Processing on a GPU

S. Sivasuthan, V. U. Karthik, A. Rahunanthan, P. Jayakumar, R. S. Thyagarajan, Lalita Udpa, S. R. H. Hoole

Publisher page

Abstract

In nondestructive defect characterization, the genetic algorithm matches measurements to computations through finite element optimization of a parametrically described defect. This poses a huge computational load. A published element-by-element (EbE) conjugate gradients (CG) method for the graphics processing unit (GPU) parallelizes the matrix solution process. However, in finite element optimization for non-destructive evaluation (NDE), thousands of simultaneous finite element matrix solutions on parallel genetic algorithm threads on a GPU are required. This challenges the memory capabilities of a GPU and results in long waiting times making the NDE technique impracticable. To address these twin time and memory problems, we revive an old EbE processing by Gauss iterations. It yields speedups of 80+ which grow indefinitely with matrix size to values much bigger than those reported for EbE CG. For the latter the reported figures were less than 4 for the practicable matrix size of 91,333, and 96 for a size of over 1 million and falling thereafter. Our EbE implementation of CG gives a speedup of 147 for first order triangular meshes. No memory issues are faced.
Source: openaire · Quality: candidate unverified · Source record ↗

Research context

OpenAlex topics: Non-Destructive Testing Techniques · Electromagnetic Simulation and Numerical Methods · Model Reduction and Neural Networks

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (28)

Show source-provided references
1. Hoole, S.R.H.: Computer Aided Analysis and Design of Electromagnetic Devices. Elsevier, New York (1989)
2. Hoole, S.R.H.: Optimal design, inverse problems and parallel computers. IEEE Trans. Magn. 27, 4146–4149 (1991)10.1109/20.105014 ↗
3. Mahinthakumar, G., Hoole, S.R.H.: A parallel conjugate gradients algorithm for finite element analysis of electromagnetic fields. J. Appl. Phys. 67, 5818–5820 (1990)10.1063/1.345974 ↗
4. Cecka, C., Lew, A.J., Darve, E.: Assembly of finite element methods on graphics processors. Int. J. Numer. Method Eng. 85, 640–669 (2011)10.1002/nme.2989 ↗
5. Kiss, I., Gyimothy, S., Badics, Z., Pavo, J.: Parallel realization of element-by-element FEM technique by CUDA. IEEE Trans. Magn. 48, 507–510 (2012)10.1109/TMAG.2011.2175905 ↗
6. Marrocco, A., Pironneau, O.: Optimum design with lagrangian finite elements: design of an electromagnet. Comput. Methods Appl. Mech. Eng. 15, 277–308 (1978)10.1016/0045-7825(78)90045-2 ↗
7. Arora, J.S., Hang, E.J.: Efficient optimal design of structures by generalized steepest descent programming. Int. J. Numer. Method Eng. 10, 747–766 (1976)10.1002/nme.1620100404 ↗
8. Hoole, S.R.H. (ed.): Finite Elements. Electromagnetics and Design. Elsevier, Amsterdam (1995)
9. Wong, M.L., Wong, T.T.: Implementation of parallel genetic algorithms on graphics processing units. In: Gen, M., Green, D., Katai, O., McKay, B., Namatame, A., Sarkar, R.A., Zhang, B.-T. (eds.) Intelligent and Evolutionary Systems. Studies in Computational Intelligence, pp. 197–216. Polish Academy of Sciences, Warsaw (2009)10.1007/978-3-540-95978-6_14 ↗
10. Robilliard, D., Marion-Poty, V., Fonlupt, C.: Genetic programming on graphics processing units. Genet. Program. Evol. Mach. 10, 447–471 (2009)10.1007/s10710-009-9092-3 ↗
11. Karthik, V. U., Sivasuthan, S., Rahunanthan, A., Jayakumar, P., Thyagarajan, R.S., Hoole S.R.H.: Finite element optimization for nondestructive evaluation on a graphics processing unit for ground vehicle hull inspection. In: Proceedings of the 2013 Ground Vehicle Systems Engineering and Technology Symposium (GVSETS). National Defense Industrial Association (2013)
12. NVIDIA Corp.: NVIDIA CUDA Prog. Guide 2.3. Online: http://www.nvidia.com/object/cudaget.html . Downloaded 29 Nov 2013
13. http://docs.nvidia.com/cuda/cuda-toolkit-release-notes/index.html . Downloaded 22 Nov 2013
14. Wu, J.W., Heng, P.A.: A hybrid condensed finite element model with GPU acceleration for interactive 3D soft tissue cutting. Comput. Animat. Virtual Worlds 15, 219–227 (2004)10.1002/cav.24 ↗
15. Hoole, S.R.H., Sivasuthan, S., Karthik, V.U., Rahunanthan, A., Thyagarajan, R.S., Jayakumar, P.: Electromagnetic device optimization: the forking of already parallelized threads on graphics processing units. Appl. Comput. Electromagn. Soc. J. 29(9), 677–684 (2014)
16. Kakay, A., Westphal, E., Hertel, R.: Speedup of FEM micromagnetic simulations with graphical processing units. IEEE Trans. Magn. 46, 2303–2306 (2010)10.1109/TMAG.2010.2048016 ↗
17. Okimura, T., Sasayama, T., Takahashi, N., Ikuno Soichiro, S.: Parallelization of finite element analysis of nonlinear magnetic fields using GPU. IEEE Trans. Magn. 49, 1557–1560 (2013)10.1109/TMAG.2013.2244062 ↗
18. Hughes, T.J.R., Levit, I., Winget, J.: An element-by-element solution algorithm for problems of structural and solid mechanics. Comput. Methods Appl. Mech. Eng. 36, 241–254 (1983)10.1016/0045-7825(83)90115-9 ↗
19. Mahinthakumar, G., Hoole, S.R.H.: A parallelized element by element Jacobi conjugate gradients algorithm for field problems and a comparison with other schemes. Int. J. App. Electromagn. Mater. 1, 15–28 (1990)
20. Carey, G.F., Barragy, E., Mclay, R., Sharma, M.: Element-by-element vector and parallel computations. Commun. Appl. Numer. Methods 4, 299–307 (1988)10.1002/cnm.1630040303 ↗
21. Saad, Y.: Iterative Methods for Sparse Linear Systems, 2nd edn. IAM Society for Industrial & Applied Mathematics, Philadelphia (2003)10.1137/1.9780898718003 ↗
22. Kiss I., Badics, Z., Gyimothy, G., and Pavo, J.: High locality and increased intra-node parallelism for solving finite element models on GPUs by novel element-by-element implementation. In: Proceedings of the IEEE Conference on High Performance Extreme Computing (HPEC), 1–5 (2012)10.1109/HPEC.2012.6408659 ↗
23. Fernandez, D.M., Dehnavi, M.M., Gross, W.J., Giannacopoulos, D.: Alternate [sic.] parallel processing approach for FEM. IEEE Trans. Magn. 48, 399–402 (2012)10.1109/TMAG.2011.2173304 ↗
24. NVIDIA Corp.: NVIDIA CUDA prog. guide 2.3. Online: http://www.nvidia.com/object/cudaget.html
25. Yablonski, D.: Numerical accuracy differences in CPU and GPGPU codes, Electr. and Comp. Engineering Master’s Theses, Northeastern University, Paper 58 (2011). http://hdl.handle.net/2047/d20001067
26. Karam, G.M., Buhr, R.J.A.: Starvation and critical race analyzers for Ada. IEEE Trans. Softw. Eng. 16(829), 843 (1990)
27. Sivasuthan, S., Karthik, V. U., Rahunanthan, A., Jayakumar, P., Thyagarajan, R.S., Udpa, L., Hoole, S.R.H.: A Script-based, parameterized finite element mesh for design and NDE on a GPU. IETE Tech. Rev. Accepted-in press (2014), Prepress published online 23 Dec. doi: 10.1080/02564602.2014.98319210.1080/02564602.2014.983192 ↗
28. Karthik, V.U., Sivasuthan, S., Rahunanthan, A., Thyagarajan, R.S., Jayakumar, P., Udpa, L., Hoole, S.R.H.: Faster, more accurate, parallelized inversion for shape optimization in electroheat problems on a graphics processing unit (GPU) with the real-coded genetic algorithm, COMPEL. Int. J. Comput. Math. Electr. Electron Eng. 34(1), 344–356 (2015)10.1108/COMPEL-06-2014-0146 ↗